Solve x^2 3x-8 6x^2-2x

Question

Simplify the expression

3 x^{3} - 86 x^{2} - 2 x

Evaluate

x^{2} \times 3 x - 86 x^{2} - 2 x

Solution

More Steps

Evaluate

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

3 x^{3} - 86 x^{2} - 2 x

Show Solution

Factor the expression

x (3 x^{2} - 86 x - 2)

Evaluate

x^{2} \times 3 x - 86 x^{2} - 2 x

Multiply

More Steps

Evaluate

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

3 x^{3} - 86 x^{2} - 2 x

Rewrite the expression

x \times 3 x^{2} - x \times 86 x - x \times 2

Solution

x (3 x^{2} - 86 x - 2)

Show Solution

Find the roots

x_{1} = \frac{43 - 1855}{3}, x_{2} = 0, x_{3} = \frac{43 + 1855}{3}

Alternative Form

x_{1} \approx - 0.023237, x_{2} = 0, x_{3} \approx 28.689904

Evaluate

x^{2} \times 3 x - 86 x^{2} - 2 x

To find the roots of the expression,set the expression equal to 0

x^{2} \times 3 x - 86 x^{2} - 2 x = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

3 x^{3} - 86 x^{2} - 2 x = 0

Factor the expression

x (3 x^{2} - 86 x - 2) = 0

Separate the equation into 2 possible cases

x = 0 3 x^{2} - 86 x - 2 = 0

Solve the equation

More Steps

Evaluate

3 x^{2} - 86 x - 2 = 0

Substitute a= 3,b= - 86 and c= - 2 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{86 \pm ( - 86 ) ^{2} - 4 \times 3 ( - 2 )}{2 \times 3}

Simplify the expression

x = \frac{86 \pm ( - 86 ) ^{2} - 4 \times 3 ( - 2 )}{6}

Simplify the expression

More Steps

Evaluate

(- 86)^{2} - 4 \times 3 (- 2)

Multiply

(- 86)^{2} - (- 24)

Rewrite the expression

8 6^{2} - (- 24)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

8 6^{2} + 24

Evaluate the power

7396 + 24

Add the numbers

7420

x = \frac{86 \pm 7420}{6}

Simplify the radical expression

More Steps

Evaluate

7420

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 1855

Write the number in exponential form with the base of 2

2^{2} \times 1855

The root of a product is equal to the product of the roots of each factor

2^{2} \times 1855

Reduce the index of the radical and exponent with 2

21855

x = \frac{86 \pm 2 1855}{6}

Separate the equation into 2 possible cases

x = \frac{86 + 2 1855}{6} x = \frac{86 - 2 1855}{6}

Simplify the expression

x = \frac{43 + 1855}{3} x = \frac{86 - 2 1855}{6}

Simplify the expression

x = \frac{43 + 1855}{3} x = \frac{43 - 1855}{3}

x = 0 x = \frac{43 + 1855}{3} x = \frac{43 - 1855}{3}

Solution

x_{1} = \frac{43 - 1855}{3}, x_{2} = 0, x_{3} = \frac{43 + 1855}{3}

Alternative Form

x_{1} \approx - 0.023237, x_{2} = 0, x_{3} \approx 28.689904

Show Solution